Bound surface limits to a function

Consider the following plot of two surfaces

Plot3D[Sin[x y], x^3 + y, x, -1, 1, y, -1, 1, PlotRange -> x, -1, 1, y, -1, 1, z, -1, 1, Mesh -> None]


How can I produce a plot where I limit the the surface plot of $sin(x y)$, to be shown only when its values are above $x^3+y$, or any other given function.

2 Answers
2

Plot3D[ConditionalExpression[Sin[x y], Sin[x y] > x^3 + y],
x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1, Mesh -> None]


To show both functions

Plot3D[ConditionalExpression[Sin[x y], Sin[x y] > x^3 + y], x^3 + y ,
x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1,
Mesh -> None, BaseStyle -> Opacity[.7]]


Plot3D[Sin[x y], x, -1, 1, y, -1, 1,
 PlotRange -> -1, 1, -1, 1, -1, 1,
MeshFunctions -> Sin[# #2] - #^3 - #2 &, Mesh -> 0,
MeshShading -> None, Automatic, BoundaryStyle -> None]


You can utilize the option RegionFunction for that:

RegionFunction

Plot3D[Sin[x y], x^3 + y, x, -1, 1, y, -1, 1,
Mesh -> None,
RegionFunction -> (x, y, z [Function] Sin[x y] > (x^3 + y))
]


reg = BoundaryDiscretizeRegion[ImplicitRegion[Sin[x y] > (x^3 + y), x, -1, 1, y, -1, 1]]; Plot3D[Sin[x y], x, y ∈ reg]

Required, but never shown

Required, but never shown

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